Preheat oven to 350 F. Heat olive oil in a large saucepan over medium heat. Brown ground beef until no longer pink. Drain grease and add in onion and garlic. Cook for a minute.
Add in crushed tomatoes, diced tomatoes, kidney beans, salt, pepper, ground cumin and chili powder. Continue to cook over medium-low heat for 15-20 minutes. Spread chili out into a large greased baking dish.
In a small bowl, combine milk and vinegar. In a large bowl, whisk together flour, cornmeal, sugar, salt and baking powder. Add in the milk vinegar mixture, vegetable oil and egg. Whisk until smooth.
Sprinkle shredded cheddar cheese over chili and pour the cornbread mixture over the chili and cheese. Bake for 30-35 minutes.
